b reiger toolkit

7/27/2019 b Reiger Toolkit

1/25


2/25

92 R.L. Breiger / Poetics 27 (2000) 91-115I . I n t r o d u c t i o n

A p r o d u c t i v e f o r m u l a t io n i n th e s o c i o l o g y o f c u l tu r e ( S w i d l e r , 1 9 8 6 ) h o l d s t h a tc u l t u r e i n f l u e n c e s a c t i o n n o t b y p r o v i d i n g t h e u l t i m a t e v a l u e s t o w a r d w h i c h a c t i o n i so r i e n te d , b u t b y s h a p i n g a re p e r t o i re o r ' t o o l k i t ' o f h a b i t s, s k i l l s a n d s t y l e s w h i c hp e o p l e u s e i n c o n s t ru c t i n g s t ra t e g ie s o f a c t io n . W h a t t h e n c a n b e s a i d a b o u t a n a l y s t so f c u l t u r e a n d i n p a r t i c u l a r o f m e t h o d s fo r cu l tu r a l ana lys i s? S ince cu l tu r a l ana lys t st o o a r e p e o p l e e n g a g e d i n c o n s t r u c t i n g s t r a t e gi e s o f a c t i o n ( f o r u n d e rs t a n d i n g s t ra t e-g i e s o f a c t i o n ) , i t w o u l d s e e m w o r t h w h i l e t o d e f i n e m e t h o d o l o g i c a l t e c h n i q u e ,w h e t h e r a p p l i e d t o c u l t u r a l s t u d i e s o r m o r e g e n e r a l l y , n o t a s a p r i v i l e g e d s p h e r e o fa u t o n o m o u s l o g ic b u t a s a n e x a m p l e o f th e u s e o f c u l tu r al s y m b o l s w h i c h , a s S w i -d l e r ( 1 9 8 6 : 2 8 3 ) w e l l a rg u e s , " c a n b e u n d e r s t o o d o n l y in r e la t i o n t o t h e s t r a te g i e s o fa c t i o n t h e y s u s t a i n " .

I n s u c h a s p i ri t o f re f l e x i v i t y I c o n s i d e r i n th i s p a p e r a v a r i e t y o f m e t h o d s a n dm o d e l s t h a t a re u s e d i n th e s t u d y o f ' p r a c t i c e t h e o r y ' . L e s s a w e l l - f o r m e d t h e o r y t h a na pro jec t , p r ac t i ce th eory has i t s o r ig ins in d ive r se s t rands o f the wr i t ings o f Bo ur -d i e u , G i d d e n s , G e e r t z , S a h l i n s , a n d d e C e r t e a u ( O r t n e r , 1 9 9 6 : 1 - 2 0 ) . F o r m y p u r -p o s e s th e ' k e y a r g u m e n t ' o f p ra c t i c e t h e o r y i s t h a t t h e m a t e r ia l w o r l d ( th e w o r l d o fa c t i o n ) a n d t h e c u l t u r a l w o r l d ( t h e w o r l d o f s y m b o l s ) i n te r p e n e tr a te , a n d a r e b u i l t u pt h ro u g h t h e i m m e d i a t e a s s o c ia t io n o f e a ch w i t h th e o t h e r ( M o h r a n d D u q u e n n e ,1 9 9 7: 3 0 9 ). T h e t e ch n i q u e s o n w h i c h I f o c u s h a v e in c o m m o n a n e m p h a s i s o n th e' d u a l i t y ' o r c o - c o n s t i t u t i o n o f e l e m e n t s a t o n e l e v e l a n d r e la t i o n s a t a n o t h e r ( h i g h e ro r l o w e r ) l e v e l o f s o c i a l a c t i o n ( a s i n m y f o r m u l a t i o n ; B r e i g e r , 1 9 7 4 ) , I h a v e t h em o s t to s a y a b o u t th e a s s e m b l a g e o f w h a t M o h r a n d D u q u e n n e ( 1 9 9 7 : 3 0 8 ) re f e r t oa s th e r e c e n t " p r o l i f e r a ti o n o f f o rm a l t h e o r i e s , a p p l i e d m e t h o d s , a n d s o f t w a r e r o u -t in e s ... th a t a l l o w t h e s t ru c t u r a l p r o p e r t i e s o f s o c i a l p h e n o m e n a t o b e c o m e v i s i b l e in[ n e w ] w a y s " . T h i s r e s t r i c t i o n t o r e l a t i v e l y f o r m a l t e c h n i q u e s i s u s e f u l f o r t h e u n -d e r s ta n d i n g a n d f u r t h e r e l a b o r a t i o n o f a n e v o l v i n g a n d v e r y r e al s u b c u l t u r e o f c u l -t u r a l a n a l y s i s , w h i c h i s m y m a i n g o a l . A t t h e s a m e t i m e , r e s t r i c t i o n t o f o r m a l t e c h -n i q u e s i s s e l f- l im i t i n g i f i t r e i n f o r c e s t h e t e n d e n c y o f t h is v e r y b r a n c h o f p r a c t i c et h e o r y t o v e e r b a c k t o w a r d t h e s t r u c t u r a l i s t m o d e s o f a n a l y s i s f r o m w h i c h i t a r o s e ,r a th e r t h a n f o r w a r d t o w a r d d i a l o g u e w i t h s t u d e n t s o f t h e m o r e l o c a l l y - b a s e d e m p h a -s i s on ac t ion - inc lud ing d i s ru p t ive and cha l leng ing ac t iv i t i e s - a s soc ia ted wi th thea n a l y s i s o f d i s c u r s i v e p ra c t i c e s ( D u r a n t i a n d G o o d w i n , 1 9 9 2 ) a n d w i t h t h e d e v e l o p -m e n t o f p r a c t ic e t h e o r y f r o m t h e p o i n t s o f v i e w o f f e m i n i s t a n d s u b a l t e rn s c h o l a rs h i p(Or tne r , 1996) . I n f ac t the r e la t ion o f a fo rm al , s t r uc tur a l ve r s ion o f p r ac t i ce th eoryt o a m o r e a c t i o n - o r i e n t e d , p r o c e s s u a l , f r a m e w o r k ( s e e a l s o E m i r b a y e r , 1 9 9 7 ) p r o -v i d e s s o m e o f t h e t e n s i o n u n d e r l y i n g t h e a r g u m e n t s o f t h is p a p e r .1 . 1 . M a t e r i a l s

A s a m o l d o r a m a t r ix f o r c a s ti n g t h e t o o l s f o r th e w o r k i n g p r a c t ic e t h e o r i s t 's k i t ,c o n s i d e r P i e rr e B o u r d i e u ' s " c o n v e n i e n t i n s t ru m e n t o f c o n s t ru c t i o n o f t h e o b j e c t : t h es q u a r e - t a b l e o f th e p e r t i n e n t p r o p e r t i e s o f a s e t o f a g e n t s o r i n s t i t u ti o n s " ( B o u r d i e u ,1992 [1988] : 230 ; o r ig ina l i t a l i c s ) . " I f , f o r example , my ta sk i s to ana lyze va r ious


3/25

R.L. Bre iger / Poe t ics 27 (2000) 91-1 15 93combat spor t s (wres t l ing , judo , a ik ido , box ing , e tc . ) , o r d i f f e r en t ins t i tu t ions o fh i g h e r l e a r n i n g , o r d i f f e r e n t P a r i s i a n n e w s p a p e r s " , B o u r d i e u ( 1 9 9 2 [ 1 9 8 8 ] : 2 3 0 )te l ls h i s g r adua te s tuden ts , " I w i l l en te r each o f these ins t i tu t ions on a l ine and I wi l lc r e a t e a n e w c o l u m n e a c h t i m e I d i s c o v e r a p r o p e r t y n e c e s s a r y t o c h a ra c t e ri z e o n e o ft h e m " . T h i s v e r y s i m p l e t ab l e (i n w h i c h t h e n u m b e r o f r o w s a n d t h e n u m b e r o fc o l u m n s w i l l l i k e l y d i f fe r , d e s p i te i ts d e s i g n a t io n a s ' s q u a r e ' ) " h a s t h e v i rt u e o f f o r c -i n g y o u t o t h i n k r e l a t i o n a l ly b o t h a b o u t th e s o c i a l u n it s u n d e r c o n s i d e r a t i o n a n d t h e i rp r o p e r t i e s " ( 1 9 9 2 [ 1 9 8 8 ] : 2 3 0 ) . S o m e w e l l - k n o w n e x a m p l e s in B o u r d i e u ' s w o r k a rea t a b l e c r o s s - c l a s s i f y i n g m a j o r F r e n c h c o r p o r a t e b o a r d s a n d t h e i r i n d i v i d u a l m e m -b e r s b y t h e i r e d u c a t i o n a l p e d i g r e e s ; a t a b l e c r o s s - c l a s s i f y i n g s u b j e c t s t h a t w o u l dm a k e a b e a u t if u l p h o to g r a p h b y t h e o c c u p a t i o n o f p e o p l e c h o o s i n g e a c h s u b j e c t; a n da t ab le ind ica t ing as co lumns the ep i the t s ( r ang ing f rom ' l ive ly ' and ' cu l t iva ted ' to' f l abby , n ice , pue r i l e ' , and wor se ) wr i t t en in g i r l s ' p rogres s r epor t s a t an e l i t e s ec -o n d a r y s c h o o l a n d , a s r o w s , t h e g i r l s ' f a t h e r s ' o c c u p a t i o n s ( ' t a x c l e r k , p r o v i n c e s ' ,a n d s o o n ; B o u r d i e u , 1 9 9 6 [1 9 8 9 ] : 3 6 2 - 3 6 3 , 1 9 8 4 [1 9 7 9 ] : 5 2 6 , 1 9 88 [ 1 9 8 4 ] :1 9 5 - 1 9 8 r e s p e c t i v e l y ) . F r o m s u c h t a b l e s o n e m a y c o n s t r u c t " s o c i a l s p a c e s w h i c h ,t h o u g h t h e y r e v e a l t h e m s e l v e s o n l y i n th e f o r m o f h i g h ly a b s tr a c t, o b j e c t i v e re l a -t io n s , . .. a re w h a t m a k e s t h e w h o l e r e a l it y o f th e s o c i a l w o r l d " ( 1 9 9 2 [ 1 9 8 8 ] : 2 3 1 ) .

I n s e c t i o n 2 o f t h is p a p e r I c o n s i d e r c o r r e s p o n d e n c e a n a l y s is , t h e q u a n t it a t iv em e t h o d w i t h w h i c h B o u r d i e u i s m o s t i d e n t i f i e d . I d o s o , h o w e v e r , b y c r o s s - r e a d i n gB o u r d i e u a g a i n s t t h e q u i t e d if f e re n t a p p r o a c h o f J a m e s C o l e m a n . I s h o w t h a t t h e re i sa r e m a r k a b l e h o m o l o g y , a t th e l e v e l o f t h e ir f o r m a l p r a c t ic e s , b e t w e e n t h e m a t h e -m a t i ca l t e c h n iq u e s o f B o u r d i e u ' s t o o l k it a n d th o s e h o n e d a t C o l e m a n ' s f o u n d r y . M yp u r p o s e i s n o t t o a s s e r t t h a t o n e a n a l y s t i s m o r e e n c o m p a s s i n g t h a n t h e o t h e r o r t o' m i s r e c o g n i z e ' ( a s B o u r d i e u m i g h t s a y ) a f f i n i t i e s a m o n g t h e m , b u t t o d e v e l o p m o r es turdy r e la t ions among the too l s in a p r ac t i ce theor i s t ' s k i t .

A s e c o n d m a i n l in e o f f o rm a l d e v e l o p m e n t i n w h i c h p r a c t ic e t h e o r y h a s b e e nm o v i n g i s th e a n a l y s i s o f d u a l ( o r G a l o i s ) l a t ti c e s. T h e d e f i n i ti v e s o c i o l o g i c a l w o r k( M o h r a n d D u q u e n n e , 1 9 9 7 ), w h i c h a p p l i e s th i s m o d e l to a st u d y o f t h e lo g i c o fc l a s s i fi c a t i o n p r a c t i c e s f o r p o o r r e l i e f i n N e w Y o r k C i t y a r o u n d t h e t u rn o f t h e c e n -t u ry , h a s n o w b e e n jo i n e d b y a m a j o r s t u d y ( M i s c h e , 1 9 9 8 ) o f m o v e m e n t s , s o c ia ln e t w o r k s , a n d t h e f o r m a t i o n o f a c i v i c c u l t u r e in B r a zi l ; M i s c h e p u s h e s G a l o i s l at -t ic e a n a l y s i s i n t h e d i r e c t i o n o f r e s e a r c h t h a t t a k e s t i m e s e r i o u s l y , a r g u i n g f o r ad y n a m i c c o n c e p t i o n o f c i v i c c u l t u r e a s th e c o n s t r u c t i o n o f i de n t i ti e s , p r o j e c t s , a n ds t y l e s o f i n t e ra c t i o n a c r o s s d i v e r s e a n d c o n t e n d i n g n e t w o r k s . O n t h e f o r m a l s i d e ,M i s c h e a n d P a t t i s o n ( t h i s i s s u e ) e x t e n d l a t t i c e a n a l y s i s t o s t u d y t h r e e - w a y i n t e r p e n -e t r a t i o n a m o n g o r g a n i z a t i o n s , p r o j e c t s , a n d e v e n t s . W i l e y a n d M a r t i n ( 1 9 9 9 ; s e ea l s o M a r t i n , t h i s i s s u e ) p r e s e n t a f o r m a l m o d e l t h a t , i n a m a n n e r o f s p e a k i n g , c o m -b i n e s a l g e b r a i c a n d s t a t i s t i c a l a p p r o a c h e s t o a l l o w u n c o v e r i n g t h e s k e i n o f ' s o c i a ll o g i c ' c o n n e c t i n g c u l t u r a l i t e m s . W i t h i n t h e g r o w i n g l i t e r a t u r e o n f o r m a l m o d e l s( F r e e m a n a n d W h i t e , 1 9 9 3 ; P a t t is o n , 1 9 9 3 : 1 3 5 - 1 7 1 ; W h i t e a n d D u q u e n n e , 1 9 9 6 ;P a t t i s o n a n d R e e v e , 1 9 9 6 ) , a n i m p o r t a n t t e c h n i c a l i s s u e , i n s e p a r a b l e f r o m s u b s t a n -t i v e c o n c e r n s , i s h o w t o s i m p l i f y t h e a l g e b r a ic s t r u c t u re o f h i g h l y c o m p l e x r e l a t io n sa m o n g s y m b o l s . I n s e c t io n 3 o f t h is p a p e r I c o n t e n d t h a t c o r r e s p o n d e n c e a n a l y s i sm e t h o d s , a n d r e l a te d s t a t i st i ca l m o d e l s , c a n h e l p h e r e . S e c t i o n s 4 a n d 5 f o c u s o n t h e


4/25


5/25

R.L. Breiger / Poetics 27 (2000) 91-115 95"On both sides of the Atlantic, the same numerical algorithms are applied to data analysis. Bibliograph-ical references cross over the ocean, but the very spirit of correspondence analysis, as we understand it,did not cross over y et." (BenzEcri, 1991 : 1115)I n d e e d , m y e s s a y c a n b e r e a d i n p a rt a s a n e f f o r t a t ' r e c o v e r i n g ' t h e s p ir it o fc o r r e s p o n d e n c e a n a l y s i s f r o m i ts E n g l i s h a n d A m e r i c a n c r it ic s in m u c h t h e s a m ew a y t h a t H o l t (1 9 9 7 ) e n d e a v o r s t o r e c o v e r B o u r d i e u ' s t h e o r y o f t a st e s f r o m i tsA m e r i c a n c r i t i c s .

B e c a u s e o f t h e c ri t i ci s m s o f c o r r e s p o n d e n c e a n a l y s i s f o r b e i n g m e r e l y d e s c r i p ti v e ,d a t a - d r e d g i n g , a n d s o f o r t h ( s e e th e h i s to r i c a l a n d a n a l y t i c a l p e r s p e c t i v e p r e s e n t e d i nv a n M e t e r e t a l. , 1 9 9 4 ) , a n d a l s o f o r o t h e r r e a s o n s s o o n to b e c o m e a p p a r e n t , I t u r nn o w t o a n a p p r o a c h t h a t s e e m s i n c e r t a in r e s p e c t s t h e a n t it h e si s o f B o u r d i e u ' s . I r e f e rt o t he p r e c is e l y f o r m u l a t e d ' m a t h e m a t i c s o f s oc ia l a c t i o n ' i n J a m e s C o l e m a n ' s F o u n -d a t i o n s o f s o c i a l t h e o r y ( 1 9 9 0 ) , w h i c h u n d e r l i e s t h e a u t h o r ' s r a t i o n a l c h o i c e p r o g r a mo f r e s e a r c h a n d t h e o r y b u i l di n g . I w i l l s h o w t h a t t h e re i s a r e m a r k a b l e h o m o l o g y - a tt h e l ev e l o f f o r m a l p r a c t i c e s , i f n o t i n d e e d i n t h ei r ' v e r y s p i ri t ' - b e t w e e n t h e m a t h -e m a t i c a l t e c h n i q u e s i n B o u r d i e u ' s t o o l k i t a n d t h o s e d e v e l o p e d m o r e e x p l i c i tl y b yC o l e m a n . M y p u r p o s e i s n o t t o a s s e r t t h a t o n e a n a l y s t is m o r e e n c o m p a s s i n g t h a n t h eo t h e r, b u t t o ra i s e a s er i es o f q u e s t i o n s , s o m e o f w h i c h I f in d t r o u b l i n g a n d s o m ep r o m i s i n g , a b o u t t h e t o o l s r e s t i n g i n a p r a c t i c e t h e o r i s t ' s k i t .

T o b e s p e c i f ic , I w i l l c o n s i d e r a n e x a m p l e t h a t a s t u de n t o f C o l e m a n ' s w o r k m i g h tf i n d c o n g e n i a l . T h e m e m b e r s o f t h e U . S . S u p r e m e C o u r t c a n b e s a id to b e d i ff e r e n -t i a l ly i n t e r e s t e d i n c a s e s e x e m p l i f y i n g v a r i o u s i s s u e s : c i v i l r i g h t s v e r s u s d u e p r o c e s si s s ue s v e r s u s e c o n o m i c i s s u e s, p e r h a p s . A n d t h e y m i g h t b e s a i d t o e x e r c i s e d i f f e r e n -t ia l a m o u n t s o f c o n t r o l in e a c h o f t h e se a r e a s. I ta k e a s m y e x a m p l e t w o t e r m s ( F a ll1 9 91 t h r o u g h S p r i n g 1 9 9 3 ) o f t h e ' R e h n q u i s t C o u r t ' , u s i n g d a t a f r o m t h e U . S .S u p r e m e C o u r t J u d i c i al D a t a b a s e ( S p a e t h, 1 9 94 ) . I d e f i n e ' i n t e r e s t ' a s t h e te n d e n c yo f a j u s t i c e t o a u t h o r o p i n i o n s n o t re q u i r e d b y t h e C o u r t a n d f o c u s e d o n c a s e s o f ap a r t i c u l a r t y p e ( c i v i l ri g h t s , d u e p r o c e s s , a n d s o o n ) . 2 I d e f i n e ' c o n t r o l ' a s t h e t e n -d e n c y o f a j u s t i c e t o b e in th e m a j o r i t y o f o p i n i o n s f o r m a l l y v o t e d u p o n b y t h e C o u r ti n e a c h r e s p e c t i v e i s s u e a r e a . T a b l e s 1 a n d 2 r e p o r t t h e d a t a r e f l e c t i n g t h e ' I n t e r e s t 'a n d ' C o n t r o l ' o f th e n i n e j u s t i c e s i n s e v e r a l a re a s ; I w i l l s o m e t i m e s r e f e r t o th e s et a b l e s a s m a t r i x X a n d m a t r i x C r e s p e c t i v e l y . 3 T h e i s s u e a r e a s I h a v e c h o s e n a r e t o o

2 The assignm ent of the writing of opinions by the chief justice to his associates is clearly an exerciseof formal authority. For this and related masons, I restrict my attention to 'special opinions', defined asthose wh ich no justice can be forced to join or prevented from joining. (O ne exam ple is a dissentingopinion; another is the writing of an opinion notwithstanding membership in the majority or pluralityopinion coalition; a more elaborate, technical definition is given in Segal and Spaeth, 1 99 3: 276-279.)Segal and Spaeth (1993: 27 9) argue that writing and joining o f special opinions "bespeak an ability topersuade or convince another of the correctness of on e's position .. . without the use o f coercion, author-ity, or political control". Work on the Supreme Court related to that presented here appears in Breigerand Roberts (1998) and in Han and Breiger (1997).3 To illustrate how Table 1 was constructed, consider the 48 cases in the area of crime that weredecided by the Supreme Court in the period of interest. In 36 of these cases Rehnquist voted with themajority, and in 15 cases Thomas voted with the majority. Thus, the proportion of cases in which Rehn-quist and Thomas voted in the majority w as .75 (= 36/48 ) and .31 (= 15/48), respectively. Table 1 norms


6/25

9 6 R.L. Breiger / Poet ics 27 (2000) 91-115

f e w a n d t o o b r o a d l y d e f m e d t o b e a d e q u a t e f o r a s e r i o u s a n a l y s i s , b u t a r e h a n d yn o n e t h e l e s s f o r m a k i n g m y p o i n t s . R e s e a r c h t h a t m o v e s c l o s e r t o ' g e t t i n g t h e t e x t '( M o h r , 1 9 9 8 ) o f d i s c u r s i v e p r a c ti c e s s h o u l d g o f u r t h e r t h a n t h e d i d a c t ic e x a m p l ec h o s e n h e r e t o w a r d u n d e r s ta n d i n g w i t h i n a r el a ti o n a l c o n t e x t h o w c o u r t s fu n c t i o n a s" m o v i n g c l a s s i f i c a t io n s y s t e m s " s u c h t h a t " t h e k i n d o f r e a s o n i n g i n v o l v e d in th el e g a l p r o c e s s i s o n e i n w h i c h t h e c l a s s i f ic a t i o n c h a n g e s a s th e c l a s s i f ic a t i o n i s m a d e "(Levi , 1949: 3 )T a b l e 1M a t r i x C o f C o n t r o l , a n d d e r i v e d v e c t o r r i o f a c t o r p o w e rJ u s t ic e M a t i x C o f C o n t r o l

C r i m e E c o n o m y C i v i l r i g h t s F i r s t a m e n d . D u e p r o c e s s( 4 8 ca s es ) ( 4 6 ca s es ) ( 3 2 ca s es ) ( 1 4 ca s es ) ( 7 ca s e s )

D e r i v e dp o w e r(ri)

Re hn qu is t .14 .11 .15 .17 .13 .138K e n n ed y . 1 4 . 1 3 . 1 3 . 1 6 . 1 3 . 1 3 7O ' C o n n o r . 1 3 .1 3 . 1 3 .1 2 . 1 3 . 1 2 5Sca l ia .13 .11 .11 .14 .13 .122Ste ven s .09 .12 .11 .14 .11 .108B l ac k m u n .11 . 1 2 . 1 0 . 1 0 . 0 5 . i 0 7W hi te .10 .10 .11 .07 .16 .103So ute r .11 .10 .10 .07 .08 .099T h o m as . 0 6 . 0 8 . 0 6 . 0 3 . 0 8 . 0 6 2To ta l 1 .00 1 .00 1 .00 1 .000 1 .00 1 .00( V o t e s ) ( 2 5 6 ) ( 2 8 7 ) ( 1 9 2 ) ( 5 8 ) ( 3 8 )

2.2. Power and value as dimensions of a spaceI n c o n s i d e r i n g C o l e m a n ' s Foundations, I u r g e r e c o g n i t i o n o f " t h e t w o - l e v e lc h a r a c t e r o f t h e t h e o r y " ( C o l e m a n , 1 9 9 0 : 6 6 7 ) . I n f a c t, C o l e m a n d o u b l e s th e d u a l-

t h e s e n u m b e r s b y u s i n g a d i f fe r e n t c o n s ta n t , h o w e v e r , j u s t to i n s u r e t h a t th e s u m o f e a c h c o l u m n i s u n i t y( s o a s t o b e c o n s i s t e n t w i t h t h e m o s t e l e m e n t a r y f o r m o f C o l e m a n ' s a l g o r i t h m t o b e a p p l i e d t o t h e s ed a t a ). T h e t o t a l n u m b e r o f v o t e s i n t h e m a j o r i ty ( f r o m c a s e s w i t h 5 - 4 s p li t s o r h i g h e r if n i n e j u s t ic e sd ec i d ed , o r s p l i t s o f 5 - 3 o r ab o v e i n t h e t h r ee ca s e s d ec i d e d b y o n l y e i g h t j u s t i ce s ) i s 2 5 6 f o r ca s e s d ea l -i n g w i t h c r i m i n a l la w . T a b l e 1 n o r m s t h e n u m b e r o f t i m e s e a c h j u s t i c e v o t e d i n t h e m a j o r it y b y t h e n u m -b e r o f m a j o r i t y v o t e s o n e a c h i s s u e re s p e c t i v e ly . H e n c e , t h e e n t r ie s f o r R e h n q u i s t a n d T h o m a s i n t h e f ir s tc o l u m n o f T a b l e 1 a r e . 1 4 ( = 3 6 / 2 5 6 ) a n d . 0 6 ( = 1 5 / 25 6 ) , re s p e c t iv e l y . T h u s , C o n t r o l o v e r a n is s u e i sd e f i n e d a s t h e t e n d e n c y o f a j u s t i c e t o p r e v a i l ( v o t e i n t h e m a j o r i t y ) o n t h a t i s s u e . T u r n i n g t o T a b l e 2( I n t e r e s t ) , t h e u n i t o f an a l y s i s i s t h e ' s p ec i a l o p i n i o n ' ( d e f i n ed i n t h e p r ev i o u s n o t e ) . A s an i l l u s t r a t i o n :o f t h e 3 6 s p e c i a l o p i n i o n s a u t h o r e d b y R e h n q u i s t i n t h e p e r i o d o f i n t e r e st , 1 2 ( o r 3 3 % ) w e r e i n t h e a r e ao f c r im e , a n d 2 ( o r 6 % ) w e r e i n t h e a r e a o f du e p r o c e s s . H e n c e , t h e e n t r i e s f o r C r i m e a n d D u e P r o c e s si n R eh n q u i s t ' s co l u m n o f T ab l e 2 a r e . 3 3 an d . 0 6 , re s p ec t i v e l y . I n t h i s w ay , I n t e r e s t is d e f i n ed a s t h e t en -d e n c y o f a j u s ti c e t o a u t h o r o p i n i o n s i n a g i v e n a r e a o f t h e l a w ( c o n f i n i n g th e m e a s u r e t o t h o s e a u t h o r e do p i n i o n s t h a t w e r e n o t r e q u i re d b y t h e C o u r t , a s d e s c r i b e d i n t h e p r e v i o u s n o t e ) .


7/25

R.L . Bre iger / Poet ics 27 (2000) 91-115

Table 2Matrix X of Interests, and derived vector vj of resource value

97

Matrix X of Interests DerivedIssue Rehnquist Kennedy O'Connor Scalia Stevens Blackmun White Souter Thomas valuevjCrime .33 .37 .37 .33 .43 .35 .50 .29 .45 .375Economy .39 .23 .23 .27 .21 .22 .21 .18 .23 .247Civil fights .11 .20 .19 .23 .20 .22 .07 .18 .19 .175Firstamend..11 .14 .16 .13 .11 .13 .21 .18 .10 .141Due process .06 .06 .05 .04 .05 .09 .00 .18 .03 .061Total 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 .00 1.000(Opinions) (36) (35) (43) (48) (56) (55) (14) (17) (31) 1.000

ity, by considering the interlacing of actors and issues with respect to two relations(interest and control) simultaneously (and to more than two in his chapter 27; onthis extension, see also Marsden and Laumann, 1977). Moreover, Coleman providesa self-consciously thin meta-narrative (in a sense intended as the exact opposite ofthe kind of 'thick' description often applied by Clifford Geertz and other practicetheorists) about action and exchange. 4 Assuming "there is no structure to impedeany actor's use of resources at any point in the system" (Coleman, 1990: 719) -that is, positing the absence o f transaction costs - actors exchange some o f theircontrol over resources they have in order to gain more of the resources they desire.Emergent from such a market-like social system are analogues to 'price', in thatCole man 's mathematics allows him to compute the ' valu e' of each resource(denoted v j ) . And dually, the 'power' of each actor (denoted ri) is also a scalar quan-tity that emerges from the 'market' of exchanges. To the extent that one actor con-trols the resources in which anothe r is interested - such control being represented inthe matrix product C X - to that extent 'power' is exercised, within Coleman'sframework.

An extensive presentation of Coleman's (1990) mathematical model appears aspart IV of his work. What is important for present purposes is the relation of Cole-man's model to correspondence analysis. The basic relation is as follows. The Cor-respondence Analysis (CA) of a matrix of relations yields a decomposition of thatmatrix into the marginal effects (i.e., functions of the one-variable distributions ofactors into row categories and into column categories) p l u s a set of dimensions thataccount for the statistical association between the row categories and the column cat-egories. Two points need to be made about the relation of CA to Coleman's model.First, Coleman's mathematical solutions for the 'power' of actors and for the 'value'of events are eigenvectors o f products of his C and X matrices, even though he never

4 "In the parsimonious conception of a system of action that I want to establish, the types of actionavailable to the actor are severely limited. All are carried out with a single purpose - to increase theactor's realization of interests" (Coleman, 1990: 32).


8/25

98 R.L. Breiger / Poetics 27 (2000) 91-115quite says so. 5 Thus, at a purely formal level, Coleman's mathematics of rationalaction and the type of CA that Bourdieu employs are mutually implicative. Second,Coleman's model yields a single set of eigenvectors ('power' and 'value' respec-tively) that pertain essentially to the marginals alone. In other words, Coleman'sanalyses of interest and control (or dually, the power of actors and the equilibriumvalues of events) exploits the one-dimensional distributions of interest and controlwhile ignoring subsequent dimensions pertaining to statistical interactions. SeeAppendix A to this paper for related discussion.2 .3 . C o n s t r u c t i n g p o w e r a n d v a l u e i n a j u r i d i c a l f i e l d : T h e s u p r e m e c o u r t

Tables 1 and 2 report Coleman' s derived constructs of 'power' and 'value' (ri andvj) along with the Control and Interest matrices (C and X, respectively). The derivedvectors of power and value were computed using the 'iterative method' given inColeman (1990: 698-700), identical to the eigenvector approach of this paper'sappendix (section A.4). From Table 1 it is seen that each number in the 'power' vec-tor is close to the average entry in its row, and a similar observation pertains to the'value' vector given in Table 2. This closeness is 'built in' to Coleman's model (andsee also section A.5 of the appendix).

The one-dimensional marginal effects embodied in Coleman's principal con-structs, while not the full picture, go a long way in guiding interpretation, even withrespect to this rather home-cooked example. It is seen that Justices Rehnquist andKennedy have the highest 'power' scores (scores in Table 1 of .138 and .137),defined operationally (implementing an idea of Coleman's within the Supreme Courtcontext) as voting with the majority in issue areas of greatest concern among the jus-tices. In fact, Rehnquist, in contrast to his predecessor as chief justice, has emergedas a highly central leader of the Court (Simon, 1995). And in the 1992-1993 termJustice Kennedy was the 'least frequent dissenter' (dissenting in five out of 107votes overall; Greenhouse, 1993). At the other extreme, Justice David Souter, whoaccording to my implementation of Coleman's measure (voting with the majority inissue areas of high concern) has low power, in fact was a frequent dissenter, dis-senting in 12 of the 17 cases decided by a 5--4 vote in the 1992-1993 term. Also atthe ' low power' end of Coleman's scale is Justice Clarence Thomas, these two yearsbeing his first on the Court following an explosive confirmation process and markedby opinions, such as his dissent from the finding that it was cruel and unusual pun-ishment to confine a non-smoking prisoner in a cell with a chain-smoker, that "tookissue with 17 years of Supreme Court precedents on unconstitutional prison condi-tions" (Greenhouse, 1993: El). Thus, Coleman's 'power' dimension for Table 1seems to make a great deal of practical sense.

Anecdotal validation of the 'value' measure in Table 2 is less straightforward. Byconstruction, the matrix X C is of dimension issues by issues, and reports the extent

5 Pullum(1975) and Marsden and Laumann (1977: 244) have noted that Coleman's mathematicalsolution for 'power' and 'value' reduces to an eigenvector problem, and Tam (1989) has taken thisinsight in substantive directions.


9/25

R.L. Breiger / Poetics 27 (2000) 91-115 99

t o w h i c h e a c h g i v e n i s s u e a r e a is c o n t r o l l e d b y j u s t i c e s w h o d e s i r e e a c h a re a . ' V a l u e 'is an e i g e n v e c t o r o f th is m a t r i x ( s ee A p p e n d i x A ) . C r i m e a n d t he e c o n o m y w e r e b yt h is c r i t e ri o n t h e m o s t v a l u e d i s s ue a r e a s a m o n g t h e j u s t ic e s , w i t h d u e p r o c e s s v a l -u e d l e a s t .I t w i l l b e in s t r u c t iv e t o c o m p a r e a n a n a l y s i s o f t h e s e d a t a d e r iv i n g f r o m C o l e -m a n ' s a p p r o a c h t o o n e b a s e d o n th e C o r r e s p o n d e n c e A n a l y s i s th a t f i gu r e s p r o m i -n e n t l y i n s o m e o f B o u r d i e u ' s w o r k . F o r th i s p u r p o s e I u s e th e ' r a w ' c o u n t s o f v o t e so n w h i c h T a b l e 1 i s b a s e d , a n d , s i m i l a rl y , t h e a c tu a l n u m b e r s o f o p i n i o n s w r i t te n( T a b l e 2 ) . 6

C o n s i d e r f i r st T a b l e 1. T h e s i m p l e r o w s u m s o f T a b l e 1 c o r r e l a te . 99 8 w i t h C o l e -m a n ' s ' p o w e r ' m e a s u r e . ( T h e ' n ' f o r th i s c o r r e l a t io n c o n s i s t s o f t h e n in e j u s ti c e s .)T h e r o w s u m s c o r r e l a t e . 9 95 w i t h th e f ir s t d i m e n s i o n o f th e S V D o f T a b l e 1 ( s eeA p p e n d i x A ) . T h e c o r r e l a t i o n o f t h is f ir s t d i m e n s i o n w i t h t h e r o w s u m s i s .9 8 9 . C o n -s i d e r n e x t T a b l e 2 , w h e r e w e h a v e o n l y f i v e is s u e a re a s . A c r o s s t h e s e f i v e, t h e r o ws u m s c o r r e l at e . 9 9 8 w i t h C o l e m a n ' s ' v a l u e ' m e a s u r e . T h e f ir st d i m e n s i o n o f t heS V D o f T a b l e 2 c o r r e l a te s . 9 9 7 w i t h t h e s e r o w s u m s , a n d c o r r el a t e s . 9 9 9 5 w i t h C o l e -m a n ' s ' v a l u e ' m e a s u r e . 7 C o l e m a n ' s p r i n c i p al e x p l a n a t o r y c o n s t r u c t s a r e e s se n t i a ll yt a p p i n g i n t o t h e m a r g i n a l s o f t h e s e t a b le s .

I t u rn n e x t t o t h e C o r r e s p o n d e n c e A n a l y s i s o f th e s e d a t a f r o m t h e S u p r e m e C o u r t ,a s t h e C A m o d e l i n c l u d e s t h e m a r g i n a l e f f e c t s ( d is c u s s e d a b o v e ) plus d i m e n s i o n sp e r t a i n in g t o t h e a s s o c i a t io n o f r o w s a n d c o l u m n s . B e c a u s e m y i n t er e s ts a r e l a r g e l yd i d a c t i c , I w i l l f o c u s o n l y o n ( t h e ' r a w ' c o u n t s o f v o t e s i n ) T a b l e 1 , t h e m a t r i x o fC o n t r o l , a n d o n t h e f ir s t t w o d i m e n s i o n s a b o v e a n d b e y o n d t h e m a r g i n a l s . 8 T h e s ed i m e n s i o n s a r e s h o w n g r a p h i c a l l y i n F i g . 1 .

A g r e a t d e a l o f t h e p o p u l a r i t y o f C A w i t h s t r u c t u r a l a n a l y s t s a n d p r a c t i c e t h e o -r is t s a l ik e d e r i v e s f r o m i ts a b il i ty t o p o r t r a y t w o t y p e s o f e n ti t y ( h e re , S u p r e m eC o u r t j u s t i c e s a n d i s s u e a r e a s ) i n t h e ' s a m e ' s p a c e . 9 G o o d m a n ( 1 9 9 6 , 1 9 9 7 ) p r o -v i d e s a w e l l - f o u n d e d i n t e r p r e t i v e f r a m e w o r k f o r C A d i a g r a m s o f t h is s o rt , o n e w i t hw h i c h p r a c t i c e t h e o r i s ts s h o u l d b e c o m e f a m i l i a r. I n o f f e r in g t h e f o l l o w i n g i n t e r p re -t a ti o n o f F ig . 1 I c u t s o m e c o m e r s ( s o t o s pe a k ) o f G o o d m a n ' s i n te r p re t iv e f r a m e -w o r k i n t h e in t e r es t o f a c o n c i s e t r e a tm e n t , w h i c h I b e l i e v e w i ll n o n e t h e l e s s s u f f i c ef o r p r e s e n t p u r p o s e s . I w i l l f o c u s o n t h e d i s t a n c e o f e a c h e n t i t y f r o m t h e o r i g in ( t h e

6 The reader ma y recover these counts by mu ltiplying the proportion given in any cell of Table 1 (orof Table 2) by the number in parentheses at the bottom of that column, and then rounding to the nearestwhole integer. See note 3 above.7 The correlation of Co lem an's power m easure with row sum s of the matrix product CX (Control xInterest) is perfectly + 1. Dually, the correlation of Colem an's value m easure with row sum s of XC (Inter-est x Control) is also perfectly +1. See also Appendix section A.5.8 Although it is standard practice among C A analysts to use the first two dim ensions, this is a higlycontentious issue with respect to tables of counted data, and very much related to the criticism .that CAis not a well-founded statistical procedure. See on these issues the development of Goodman's (1987,1996) powerful framework, and also the comments of van M eter et al. (1994).9 Indeed, the C A m odel posits that entities of one type (justices, for exam ple) have scores that are theweighted averages o f scores of the other type (issue areas, say), where the w eights are the proportions inthe data table. In this sens e the justices 'ar e' the issu e areas, and vice versa.


10/25

100 R .L. Bre iger / Poe t ics 27 (2000) 91- 115I I , l S

l a . l . . . . .

0 . B 5 . . . . . . . . . . . . . t

o /- e . i s ~ - . . . . .|D

xT H O M A S

- g . ; FI/

- 0 . 1 5 /

- E l . Z . 5 2- . - m . 1 5

I IB L A C K M U N X

L

E c o n o m i cx

x S T E V E N S 1 s t A m e n d . xS O U T E Rx ! K E N N E D Y

O ' C O N N O I ~ I :, S C A L I A

x C i v i l R i g h t s

x B . W H I T E

x R E H N Q U I S T t!!

D u e P r o c e s sx

!

I I- e . I - E . 1 1 5 B I I . 1 1 5D X M E N S Z O N I I B . I . I ; I . 1 5 1 1 1. 2 B . 2 5

Fig . 1 . Correspo ndence ana lys is (f i rs t two d im ens ion s) of the Co ntrol matr ix( the vote co unts of Table 1).


11/25

R.L. Breiger / Poetics 27 (2000) 91-115 101p o i n t [ 0, 0] o n t h e g r a p h ) a n d o n t h e c l o s e n e s s o f th e a n g l e b e t w e e n a n y t w o e n t it ie sa n d t h e o r i g in . T h e s h o r t l e n g t h o f th e p r o j e c t i o n o f ' c r i m e ' o n t o t he v e c t o r f o r m e db y J u s t i c e S c a l i a a n d th e o r i g i n d e p i c t s a s tr o n g s t a t i s ti c a l a s s o c i a t i o n : w i t h r e s p e c tt o t h e s e d a ta , S c a l i a te n d e d t o v o t e w i t h th e m a j o r i t y w h e n t h e c a s e c o n c e m e d c r i m -i n a l l a w .

T h e a n g l e b e t w e e n B l a c k m u n a n d S t e v e n s i s s m a l l ( h a s a l a r g e c o s i n e ) , r e f l e c t i n ga h i g h d e g r e e o f c o r r e l a ti o n b e t w e e n t h e s e t w o j u s ti c e s w i t h r e s p e c t t o t h e ir c o n t r olo v e r i s su e a r e a s . E x t e r n a l e v i d e n c e s u g g e s t s t h a t B l a c k m u n a n d S t e v e n s a r e ' t h eC o u r t ' s t w o m o s t l i be r a l m e m b e r s ' ( G r e e n h o u s e , 1 9 92 ). S i m i l a rl y , S c a l ia a n d R e h n -q u i s t a r e s e e n f r o m F i g . 1 t o b e h i g h l y c o r r e l a t e d , a n d t h e y ( a l o n g w i t h J u s ti c eT h o m a s ) a r e t h e m o s t c o n s e r v a t i v e m e m b e r s o f t h e C o u rt . M o r e o v e r , th e a n g l eb e t w e e n t h e B l a c k m u n - S t e v e n s d y a d a n d t h e R e h n q u i s t - S c a l i a d y a d i s q u i t e l a r g e ,s u g g e s t i n g t h a t t h e s e t w o d y a d s a r e ' f a r a p a r t ' i n t h e s p a c e o f j u d i c i a l c o n t r o l p o r -t r a y e d i n F i g. 1. A n d f u r t h e r m o r e , B l a c k m u n a n d R e h n q u i s t a r e f u rt h e r a w a y f r o mt h e o r i g i n t h a n a r e S t e v e n s a n d S c a l i a , s u g g e s t i n g ( w i t h r e s p e c t t o b o t h t h e d i a g r a ma n d t h e s o c i a l s p a c e ) t he d e f i n i n g o f a x es . T h e t h r ee n e w e s t m e m b e r s o f t he C o u r t -O ' C o n n o r , K e n n e d y , a n d S o u t e r - h a v e ' l o w ' p r o f i le s ( th e y ar e c l o s e t o t h e g r a p h ' so r i g i n ) ; t h e o t h e r a s p e c t t h e y h a v e i n c o m m o n i s t h a t t h e i r l o c a t i o n s a r e a l l r a t h e ro r t h o g o n a l f r o m b o t h t h e l i b e r a l a n d c o n s e r v a t i v e c o r e s . T h i s o r t h o g o n a l i t y f o u n ds o c i a l e x p r e s s i o n i n th e b e h a v i o r , f o r e x a m p l e , o f J u s t i c e S o u t e r i n t h e t e r m e n d i n gi n J u n e 1 9 9 3 : i n 4 0 c a s e s in w h i c h S c a l i a a n d B l a c k m u n w e r e o n o p p o s i t e s i d e s, th em o d e r a t e S o u t e r v o t e d w i t h S c a l i a i n 5 6 p e r c e n t a n d w i t h J u s t i c e B l a c k m u n i n 4 4p e r c e n t ( G r e e n h o u s e , 1 9 9 3 ). ~ J u s t i c e T h o m a s ( d i s c u s s e d a b o v e ) a n d J u s t i c e W h i t e ,w h o b y 1 99 3 w a s b y f a r th e l o n g e s t - s e rv i n g m e m b e r o f th e C o u r t a n d a b o u t t o re t ir e ,a r e l o c a t e d a p a r t f r o m e a c h o t h e r a n d f r o m t h e o t h e r j u s t ic e s .

I n b r i e f : t h e C A d i m e n s i o n s r e f l e c t s im i l a r i ti e s o f s t y l e a n d p r o f i l e th a t a r e n od o u b t r e l a te d t o C o l e m a n ' s c o n c e p t o f a c t o r ' p o w e r ' , b u t r e l a te d m o r e i n d i re c t l y t h a na r e t h e m a r g i n a l s o f T a b l e 1, o n w h i c h C o l e m a n f o c u s e s i n e s s e n c e e x c l u s i v e l y . ~lB o t h C o l e m a n ' s a p p r o a c h a n d t h e C A a p p r o a c h e x p l o i t a d u a l it y th a t is r e l e v a n t f o rp r a c t i c e a n a l y s t s , b u t t h e y d o s o i n d i s t i n c t i v e l y d i f f e r e n t w a y s . C o l e m a n f o c u s e s o nd e f i n i n g p o w e r a n d v a l u e w i t h r e s p e c t t o t h e magnitudes o f t w o r e l a t io n s ( i n t e r e s ta n d c o n t r o l ) t h a t c r o s s - c u t a c t o r s a n d r e s o u r c e s . C A f o c u s e s o n t h e similaritiesa m o n g e n t i ti e s o f d i f f e r e n t ty p e s ( s u c h a s a c t o rs a n d r e s o u r c e s ) m a p p e d i n t o a c o m -m o n s p a c e o f p r o f i l e a n d d i s t in c t i o n . C o l e m a n ' s a n a l y s i s is m o r e s o p h i s t i c a t e d t h a nt h at o f B o u r d i e u i n th a t C o l e m a n ' d o u b l e s ' t h e d u a li t y b y s t ud y i n g m a p p i n g s o fa c t o r s a n d r e s o u r c e s w i t h r e s p e c t t o t w o r e l a t i o n s ( i n t e r e s t and c o n t r o l ) . A t t h e s a m et im e , B o u r d i e u ' s a n a l y s i s i s m o r e s o p h i s ti c a te d t h a n t h at o f C o l e m a n ' s i n th a t B o u r -d i e u m o v e s b e y o n d t h e ' m a r g i n a l ' m a g n i t u d e s t o s t u dy th e association o f a c t o r s w i t h

~0 Sim on 1995: 12) writes of O'Connor, Suiter, and Kenne dy: "their secret collaboration,unknown toany o f their colleagues, produced a joint opinion in the 1992 cas e of Planned parenthood of Southeast-ern Pennsylvania v. Casey, which preserved Roe - and stunned Rehnquist and Sca lia".H The first dimension of the CA (with respect to the row s space of the Con trol matrix) correlates .61with Colem an's 'pow er' dimension reported in Ta ble 1, and (w ith respect to the c olumn space of Con-trol) .31 w ith the 'value ' scores of Tab le 1.


12/25

102 R.L. Breiger / Poetics 27 (2000) 91-115resources (so to speak 'above and beyond' the marginal distributions), and moreoverhe does so within a space that is multidimensional.

3 . T h e d u a l l a t t i c e s t r u c t u r e o f so c i a l f i e l d sSome seemingly unlikely correspondences between Pierre Bourdieu's use of anempirical, data-analytic method and James Coleman's formulation of a model of

rational choice have provided the focus of the previous section. Implications forsocial theory are drawn in section 4. There are also implications for related methodsdeployed by practice theorists. I will now draw out those implications with referenceto a technique - termed Galois lattice or concept lattice analysis - that in the workof Mohr and Duquenne (1997) and Mische and Pattison (this issue; Mische, 1998)has produced fundamental insights about the co-constitution of symbols and socialaction. Like correspondence analysis, Gallois lattice representations are very handyfor studying the association of phenomena at different levels (such as Supreme Courtjustices and issue areas). Moreover, unlike statistical approaches, the lattice is analgebraic object that is 'purely' structural. There are some practical problems withlattice analysis, however, such as the fact that lattice models quickly become highlycomplicated when applied to real data of interest, and require data in binary form. Iwill show how correspondence analysis can help with these problems (see alsoBreiger and Pattison, 1999).3 . 1 . H o w t o c o n s t r u c t a n d i n t e r p r e t a G a l o i s l a t t ic e

A Galois lattice (Davey and Priestley, 1990) is a means for representing twoorders of information in the same diagram, such that every point in the diagram con-tains information on both orders simultaneously. This lattice representation is rele-vant for the data contexts introduced in section 1.1 above in the case that the dualconnections are all of a binary nature (consider for example the table relating epi-thets written in each girl's progress report to her father's occupation).

To understand why practice theorists like dual lattices, consider Table 3, which(in the form of its first six rows) is a binary version of the Supreme Court 'Control'matrix of Table 1. I will soon detail how Table 3 is derived from Table 1, but at thispoint in my exposition I will simply take Table 3 as 'given' . The Galois lattice con-structed from Table 3 may be represented as in the diagram of Fig. 2, and I willexplain the relation between the table and the diagram. It is assumed that both Rehn-quist and Scalia tend to vote in the majority in the areas of Crime, Civil Rights, FirstAmendment, and Due Process; that is why their names are combined in row (1), andentries of ' 1' appear in the respective cells of row (1).

To construct a Galois lattice from Table 3 (first six rows), we begin with the firsttwo rows and examine their intersection (the set of issues on which the justicesindexed by the first two rows jointly tend to vote with the majority). Thus compar-ing (Rehnquist and Scalia) with Justice Kennedy, we observe that Kennedy's issues(criminal and First Amendment cases) are exactly a subset of those in row (1). In this


13/25

R .L . B re i ge r / P oe t i c s 27 ( 2000) 91 -11 5

T a b l e 3A m o d e l o f C o n t r o l , a s d e s c r i b e d i n s e c t i o n 3 .2

103

I s s u e a r e aC i v i l F i r s t

L a b e l J u s t i c e (s ) C r i m e E c o n o m y r i g h ts a m e n d .D u ep r o c e s s

( 1 R e h n q u i s t , S c a l i a 1 0 1 1 1( 2 ) K e n n e d y 1 0 0 1 0( 3 ) O ' C o n n o r , W h i t e 0 0 1 0 1( 4 ) S t e v e n s 1 1 0 1 0( 5 ) B l a c k m u n 0 1 0 1 0( 6 ) S o u t e r , T h o m a s 0 1 0 0 1(1)/x (5) 0 0 0 1 0(1) A (6) 0 0 0 0 1(2) A (3) 0 0 0 0 0(4) A (6) 0 1 0 0 0Universal 1 1 1 1 1

s e n s e , t h e i n t e r s e c t i o n o f r o w s ( 1 ) a n d ( 2 ) is r o w ( 2 ). B e c a u s e K e n n e d y t e n d s t o p r e -v a i l o n i ss u e s w h i c h a r e a s u b s e t o f th o s e i n w h i c h R e h n q u i s t a n d S c a l i a p r e v a i l, w er e p r e s e n t K e n n e d y ' b e l o w ' R e h n q u i s t a n d S c a l i a in th e G a l l o is l a tt ic e d i a g ra m o fF ig . 2 .

I n th is w a y w e s y s t e m a t i c a l l y c o m p a r e al l p a ir s o f ro w s i n T a b l e 3 . W h e n w ee n d e a v o r t o c o m p a r e r o w ( 1 ) a n d r o w ( 5 ), h o w e v e r , w e f i n d a n i n t e r se c t io n ( c o n -t a in i n g o n l y t h e F i r st A m e n d m e n t c a s e s ) t h at d o e s n o t c o r r e s p o n d t o a n y o f th e r o w si n th e g i v e n t a b l e ( t h e f ir s t s i x r o w s o f T a b l e 3 ). W e d e a l w i t h t h i s b y a d d i n g t h e n e wi n t e r s e c t i o n t o o u r o r i g i n a l t a b l e ( s e e t h e s e v e n t h r o w i n T a b l e 3 , w h i c h i s t h e f i r s t' n e w ' r o w ) , a n d w e r e p r e s e n t th is ' n e w ' r o w a s a p o i n t ( o n e n o t la b e l e d b y j u s t i c e s 'n a m e s ) ' b e l o w ' r o w s ( 1 ) a n d ( 5 ) i n th e d i a g r a m o f F ig . 2 . ( S e e t h e p o i n t i n F i g . 2l a b e l e d ' F i r s t A m e n d m e n t ' . ) . I n c o n s t r u c t i n g a G a l o i s l a t t i c e i n t h i s w a y w e c o n s i d e ri n t e r s e c t i o n s o f a l l p a ir s o f r o w s , t h o s e i n t h e o r i g i n a l d a t a s e t a n d t h o s e w e a d j o i n t oi t b e c a u s e t h e y r e p r e s e n t i n t e r se c t i o ns o f r o w s a l r e a d y c o n s i d e r e d . B y m e a n s o f th isc o n s t r u c t i o n w e o b t a i n a n o b j e c t t h a t is c l o s e d u n d e r t h e o p e r a t i o n o f ta k i n g i n t e r -s e c t i o n s . W e a l s o a l w a y s a d d i n t h e U n i v e r s a l e l e m e n t ( h a v i n g 1 s i n a l l c e l l s; s e et h e l a s t r o w l i s t e d i n T a b l e 3 ) . I n c o n s t r u c t i n g t h e l a t t i c e d i a g r a m ( F i g . 2 ) , w e p o r -t r a y e a c h r o w a s a p o i n t , p l a c i n g e a c h p o i n t b e n e a t h t h o s e i n w h i c h i t i s i n c l u d e d ( o ri d e n t i f y i n g it w i t h t h o s e t h a t a r e i d e n t i c a l, a s i s t h e c a s e i n t h is e x a m p l e w i t h R e h n -q u i s t a n d S c a l i a ) , a n d c o n n e c t i n g t w o p o i n t s w i t h a d o w n w a r d - s l o p i n g l in e i f t h eh i g h e r p o i n t c o n t a i n s t h e l o w e r o n e a n d i s m o s t s i m i l a r t o i t .

H e r e i s t h e ' p u n c h l i n e ' o f th e m a t h e m a t i c s o f t h e G a l o i s l a tt ic e . S u p p o s e w e h a ds t a r te d w i t h i s s u e s i n s t e a d o f j u s t i c e s ( i. e ., b y c o n s i d e r i n g i n t e r s e c t i o n s o f columns o fT a b l e 3 , in s t e a d o f i n t e r s e c t i o n s o f r o w s ) . T h e n i t i s n o n e t h e l e s s g u a r a n t e e d t h a t th esame l a t ti c e d i a g r a m ( F i g . 2 , in o u r e x a m p l e ) r e p r e s e n t s t h e i s s u e s ] ( S e e t h e ' F u n d a -m e n t a l t h e o r e m o n c o n c e p t la t t ic e s ' ; D a v e y a n d P r ie s t l e y, 1 9 9 0 : 2 2 4 ; o r F r e e m a n


14/25

104 R~L. Breiger / Poetics 27 (2000) 91 -11 5

R e h n q u i s t ,Sc a l i a

O ' C o n n o r , W h i teC I V IL R I G H T S

D U E P R O C E S S

{u}

C R I M E

{o}

Stevens

B i a e k m u n

E C O N O M Y

Fig. 2. G alois lattice representation of Tab le 3.a n d W h i t e , 1 9 9 3 .) W e n e e d o n l y t o r e a d t h e d ia g r a m i n th e o p p o s i t e o ri e n ta t io n . A st o j u s t i c e s , R e h n q u i s t a n d S c a l i a a re t o w a r d t h e t o p b e c a u s e t h e y p r e d o m i n a t e o n t h es a m e i s s u e s ( a n d m o r e ) a s d o t h o s e j u s t i c e s li st e d b e l o w t h e m ( O ' C o n n o r , W h i te ,a n d K e n n e d y ) . A s t o i s s u e s , d u a l l y , D u e P r o c e s s i s b e l o w Civi l R igh ts in F ig . 2b e c a u s e a ll t h e j u s t i c e s a s s o c i a t e d w i t h C i v i l R i g h t s a r e i n c l u d e d a m o n g t h o s e a s s o -c i a t e d w i t h D u e P r o c e s s . ( I n T a b l e 3 , t h e c o l u m n f o r C i v i l R i g h t s i s a s u b s e t o f t h ec o l u m n f o r D u e P r o c e s s . ) T h e ' p u n c h l i n e ' , t h e r e f o r e , i s t h a t G a l o i s l a t t i c e d i a g r a m ss u c h a s F i g . 2 p r o v i d e a n u n d e r s t a n d a b l e m e a n s f o r l o c a t i n g o b j e c t s a t d i f f e r e n tl e v e l s o f a n a l y s i s ( s u c h a s ju s t i c e s a n d i s s u e s ) w i t h i n a s i n g l e h i e ra r c h y o f c o - c o n s t i -tu t ion .


15/25

R.L. Bre iger / Poe t ics 2 7 ( 2000) 91 -115 10 5

3.2. Tasks and tools: Lattices and dimensional structureMolar and Duquenne (1997) had data of a different sort than Table 3: not zeros

and ones, but counts of the references made by organizations to their poverty prac-tices (e.g., giving food, finding a job) and to their client types (destitute, stranger,and so on). Because lattice analysis seems to require binary data, the authors (1997:317) treated all numbers greater than zero as 'present'. Using different cutoff values(greater than 2? Or perhaps 'filling in' some of the zero cells from marginal valueson the assumption that small counts 'might' have been 'missed' by the sampling pro-cedure?) 'ought' not to matter too much, in the sense that the cutoff criterion mightbe conceived as governing the 'graininess' of the representation rather than its majorcontours.

The issue of how to binarize relates to another of much greater concern. Althoughthe duality of the Galois representation is appealing, diagrams such as the onedescribed above (Fig. 2 and Table 3) can become prohibitively large. 12 Much of therecent algebraic work on lattice analysis (e.g., articles by Freeman, Duquenne andWhite in White and Duquenne, 1993; Pattison, 1993; Pattison and Reeve, 1996)seeks formal methods of simplification.

This brings us back to data on counts, and to our concern with correspondenceanalysis and related methods. There are deep relations between eigenvectors anddimensional representations, on the one hand, and lattices, on the other (Breiger andPattison, 1999). As an alternative to more complex algebraic models, Pattison and Isuggest that we might search instead to make the data simpler. As a technique tofocus on row-column association (by so to speak factoring out the marginal effects),existing models such as CA or somewhat related techniques of log-linear modeling(Goodman, 1996) might well be employed in a new way.

Specifically, in order to think of the Supreme Court data in Table 1 (actually, theraw counts on which this table was based; see note 6) as a candidate for Galois lat-tice analysis, I fitted Goodman's two-dimensional association model to these counts,and then examined expected frequencies divided by marginal parameters, in order tofocus on the 'part' of each fitted count that results solely from its situation withrespect to the two postulated dimensions. Although other choices are possible, Ibinarized these parameters at zero (taking any association between rows andcolumns to index the presence of a relationship). This is how Table 3, discussedextensively above, was generated from (the raw counts underlying) Table 1. The rel-atively small size of Table 3, including the 'new' rows added by the constructionprocess described above, suggests at least for this example that the process ofrestricting attention to row-column interactions 'net' of the marginal effects leadsto a reduction of complexity with respect to the lattice resulting from the analysis(Fig. 2).

Perhaps the greatest contribution of Fig. 2 is to illustrate that Galois latticesand correspondence analysis (along with related techniques of loglinear model-~2 E v e n f o r t h e i l lu s t r a t i v e ex am p l e s t u d i ed b y F r eem an an d Wh i t e ( 1 9 9 3 : 1 3 7) , co n s i s t i n g o f j u s t 1 8w o m en an d 1 4 g r o u p s , t h e s i ze o f t h e G a l o i s l a t t i c e r ep r e s en t a t i o n w as 6 5 e l em en t s .


16/25

106 R .L. Bre iger ! Poe t ics 27 (2000) 91-1 15

i n g ) a r e n o t a s d i f f e r e n t a s m i g h t h a v e b e e n t h o u g h t . B o t h r e p r e s e n t a t i o n s c o m -p r e h e n d t h e c r o s s - c u t t i n g n a t u r e o f e n t it i e s o f d if f e r e n t ty p e s ; b o t h t e c h n i q u e s a r es u i t a b le f o r p r a c t ic e t h e o r y . F r o m F i g . 2 w e l e a r n ( i f w e f o c u s o n l y o n t h e p o s i -t i v e in t e r a c ti o n s a s d e f in e d a b o v e ) , f o r e x a m p l e , t h a t R e h n q u i s t a n d S c a l i a te n d e dt o v o t e i n t h e m a j o r i t y i n t h e s a m e i s s u e a r e a s . R e a d i n g d o w n t h e d i a g r a m , t h e s ea r e a s w e r e : c r i m e , c i v i l r i g h t s , f i r s t a m e n d m e n t c a s e s , a n d t h o s e r a i s i n g d u ep r o c e s s q u e s t i o n s . B l a c k m u n v o t e d i n t h e m a j o r i t y o n t h e s u b s e t o f i s s u e a r ea s i nw h i c h S t e v e n s t e n d e d t o p r e v a i l ( s p e c i f i c a l l y , t h e d i a g r a m r e v e a l s t h a t B l a c k m u n ,u n l i k e S t e v e n s , t e n d e d n o t to v o t e w i t h th e m a j o r i t y i n c r im i n a l l a w c a s e s ) . M o r e -o v e r , R e h n q u i s t -S c a l i a a n d S t e v e n s - B l a c k m u n t e n d e d n o t to ' i n t e r s e c t' b y a p p e a r -i n g in t h e m a j o r i t y i n a n y i s s u e a r e a (t h e i n t e rs e c t i o n o f R e h n q u i s t a n d B l a c k m u ni s t h e ' n u l l ' n o d e a t t h e b o t t o m o f t h e d ia g r a m ) . I n s o m e t h i n g o f t h e s p i ri t o f M i s -c h e ' s ( 1 9 9 8 ) u s e o f c o r r e s p o n d e n c e a n a l y s i s to s t u d y a d i f f e re n t p r o b l e m ( th ee v o l u t i o n o f s t u d e n t m o v e m e n t s i n B r a z i l ) , i t o u g h t t o b e p o s s i b l e t o u s e F i g . 2a n d r e l a t e d d a t a o n s u c c e s s i v e t i m e p e r i o d s t o s t u d y t h e e v o l u t i o n o f c o a l i t i o n sa m o n g t h e j u s t i c e s ( s e e a l s o M i s c h e a n d P a t t i s o n , t h is i s s u e ). F i g . 2 s h o w s , f o re x a m p l e , t h a t a t o n e h i s t o ri c a l m o m e n t J u s t i c e S o u t e r te n d e d t o j o i n w i t h S t e v e n s ,B l a c k m u n , a n d T h o m a s i n v o t i n g i n t h e m a j o r i t y o n e c o n o m i c i s s u e s , w h i l e h et e n d e d t o j o i n w i t h O ' C o n n o r , W h i t e , R e h n q u i s t , S c a l ia , a n d T h o m a s i n v o t in g i nt h e m a j o r i t y o n d u e p r o c e s s i s su e s . C o n j u n c t u r e s o f i s s u e s a n d i n d iv i d u a l s s u c h a st h e s e s u g g e s t h y p o t h e s e s a b o u t t h e u n f o l d i n g d y n a m i c s o f a s o c i a l f i e l d , a n d i np a r ti c u la r a b o u t th e r o l e o f th e s o - c a l l e d m o d e r a t e s ( s e e a ls o G r e e n h o u s e , 1 9 9 2 ;S i m o n , 1 9 9 5 ) .

4 . I m p l i c a t io n s f o r p r a c ti ce t h e o r y o f t h e m e t h o d s o f B o u r d i e u a n d C o l e m a nT h e f o l l o w i n g m o r e g e n e r a l - a n d to m e i n s o m e in s t a n c e s m o r e t ro u b l i n g - c o m -

m e n t s a b o u t t h e i m p l i c a t io n s f o r p ra c t i c e t h e o r y o f th e s e f o r m a l m o d e l s a l s o s e e mwar ran ted .F i rs t , i t i s p o s s i b l e t o u s e t h e d i s c u s s i o n o f s e c t i o n 2 t o s u p p o r t a r g u m e n t s t o t h ee f f e c t t h at , " d e s p i t e h i s d i s c l a im e r s , B o u r d i e u d o e s i n d e e d s h a re a g o o d d e a l w i t hG a r y B e c k e r a n d o t h e r r a t i o n a l c h o i c e t h e o r i s t s " ( C a l h o u n , 1 9 9 3 : 7 1 ) , o r r e l a t e dc o n c e r n s t h a t , a s a p ra c t i c e t h e o ri s t, B o u r d i e u s t u d ie s p r a c t ic e s t h a t " t h e m s e l v e s a r el a r g e ly u t i li ta r ia n a n d e c o n o m i s t ic , w i t h a c t o r s s e e k i n g t o m a x i m i z e v a r i o u s f o r m s o fc a p i t a l t o e n h a n c e t h e i r o w n p o s i t i o n s " w i t h i n s t r u c t u re s ( O r t n e r, 1 9 9 6 : 4 ) . T h e p r e -s e n t p a p e r c o u l d b e u s e d t o s u p p o r t s u c h a r g u m e n t s i n t h e f o l l o w i n g w a y . I n d e v e l -o p i n g h i s m o d e l o f p o w e r a n d v a lu e , C o l e m a n ( 1 9 9 0 : 6 8 1 - -6 8 7 ) d ir e c t ly a p p l i e sc o m p e t i t i v e e q u i l i b r i u m t h e o r y f r o m e c o n o m i c s . I n a c o m p e t i t i v e e q u i l i b r i u m , e a c hgood ( r ead : r e source ) has a s ing le p r ice ( r ead : va lue ) , the r a te a t which i t i se x c h a n g e d i n a ll t r a n sa c t io n s . E a c h a c t o r m a x i m i z e s u t il i ty s u b j e c t t o a r e s o u r c e c o n -s t ra i n t (r e a d: p o w e r ) w h i c h i s e q u a l t o th e s u m o f g o o d s p o s s e s s e d w e i g h t e d b y th e i rp r i c e ( r e a d : t h e s u m o f r e s o u r c e s c o n t r o l l e d w e i g h t e d b y t h e ir v a l u e ). F u r t h e r m o r e ,t h e ' s o l u t i o n s ' f o r p o w e r a n d v a l u e i n C o l e m a n ' s s y s t e m a r e ( a s s e e n i n s e c t i o n 2 . 2a n d i l l u s tr a te d i n s e c t i o n 2 . 3 ) d u a l e i g e n v e c t o r s i n t i m a t e l y r e l a t e d t o t h e C o r r e s p o n -


17/25

R.L. Breiger / Poetics 27 (2000) 91-115 107d e n c e A n a l y s i s o f t e n e m p l o y e d b y B o u r d i e u . 13 L a s h ( 1 9 9 3 : 1 9 5 ) o f f e r s a s u i t a b lem e t a - n a r r a t i v e a l o n g t h e s e l i n e s a s t o " j u s t h o w B o u r d i e u ' s f i e l d s ( a n d m a r k e t s )w o r k " . F i e l d s a r e s it e s o f c o l l e c t i v e s y m b o l i c s t r u g g l e s a n d i n d i v i d u a l s tr a t e g ie s , a n d" t h e v a l u e o f a s y m b o l i c g o o d d e p e n d s u p o n t h e v a l u e a s s i g n e d t o it b y th e r e l e v a n tc o n s u m e r c o m m u n i t y " . V i c t o r y i n a s y m b o l i c s t r u g g l e , i n L a s h ' s i n t e r p r e t a t i o n o fB o u r d i e u , m e a n s t h a t o n e ' s s y m b o l i c g o o d s h a v e b e e n j u d g e d t o p o s s e s s m o r e v a l u et h a n t h o s e o f o n e ' s c o m p e t i t o r s . I t i s a ls o p o s s i b l e t o u s e t h e d i s c u s s i o n o f t h is p a p e rt o r e f u t e t h e c h a r g e t h a t B o u r d i e u ' s r e l i a n c e o n c o r r e s p o n d e n c e a n a l y s i s i s e c o n o -m i s t ic ( s e e m y f o u r t h o b s e r v a t io n b e l o w ) .

S e c o n d , a n d e n t i r e l y a p a rt f r o m a n y i m p u t a t io n s c o n c e r n i n g t h e r o l e o f i nd i v id u -a l s ' r a t i o n a l i t y i n B o u r d i e u ' s s o c i o l o g y , i t i s p o s s i b l e t o s e e t h e e i g e n s t r u c t u r e o f C Aa n d i ts r e l a t io n t o e q u i l i b r i u m i d e a s a s h e l p i n g t o c l a r i f y B o u r d i e u ' s c o n c e p t s o f' f i e l d ' a n d o f ' h a b i t u s ' . B o u r d i e u ( 1 9 9 0 a [ 1 9 8 0 ] ) s e e m s t o u n d e r s t a n d t h e h a b i t u s a sa c o n c e p t o f e q u i l i b r i u m , a s w h e n h e s p e a k s o f it as " a m a t r ix g e n e r a t i n g r e s p o n s e sa d a p t e d i n a d v a n c e t o a l l o b j e c t i v e c o n d i t i o n s i d e n t i c a l t o o r h o m o l o g o u s w i t h t h e( p a s t ) c o n d i t i o n s o f it s p r o d u c t i o n ; i t a d j u s ts i t s e l f to a p r o b a b l e f u t u r e w h i c h i ta n t i c i p a t e s a n d h e l p s t o b r i n g a b o u t b e c a u s e i t re a d s i t d i r e c t l y in t h e p r e s e n t o f th ep r e s u m e d w o r l d , t h e o n l y w o r l d i t c a n e v e r k n o w " ( B o u r d i e u , 1 9 9 0 a [ 1 9 8 0] : 6 4 . I nt h e a n a l y s i s o f a h a b i t u s , i t i s n e c e s s a r y t o u n c o v e r p r i n c i p l e s o f a c t i o n t h a t o r g a n i z ef i e l d s o f a c t i v i t y b o t h s p a t i a l l y a n d t e m p o r a l l y . F o r e x a m p l e , o n t h e b a s is o f B o u r -d i e u ' s ( 1 9 8 8 [ 1 9 8 4 ] : 4 8 ) s t u d y , ' t h e u n i v e r s i t y f i e l d ' i n F r a n c e m a y b e s a id t o b eo r g a n i z e d a c c o r d i n g t o tw o p r i n c i p l e s o f h i e r a r c h i z a t i o n : t h e s o c ia l h i e r a r c h y( r e f l e c t i n g t r a j e c t o r i e s t h r o u g h t h e e l i t e s e c o n d a r y s c h o o l s y s t e m i n F r a n c e , f a t h e r ' so c c u p a t i o n a n d a p p e a r a n c e i n W h o ' s w h o , a n d s o o n ) , a n d ' t h e s p e c i f i c , p r o p e r l y c u l-t u r a l h i e r a r c h y ' r e f l e c t i n g s c i e n t i f i c a u t h o r i t y a n d i n d i v i d u a l r e n o w n . C o r r e s p o n -d e n c e a n a l y s i s b r i n g s t h e s e t w o c o n c e p t s t o g e t h e r : t h e p r i n c i p l e s o f a c t i o n i d e n t i f ie dw i t h t h e d i m e n s i o n s o f C A a r e s e e n ( as i n t h is p a p e r ' s a p p e n d i x ) t o p r o v i d e ' b e s t 'r e p r e s e n t a t i o n s , a t e q u i l i b r i u m , o f a n e n t i r e r e la t i o n a l f i e l d ( o r ' b u n d l e o f r e l a t io n s ' ,B o u r d i e u a n d W a c q u a n t , 1 9 9 2 : 1 6) .

T h i r d , n o w t u r n in g t h e sp o t li g h t o n C o l e m a n ' s m a g n u m o p u s , t h e n e w a n d i m p o r -t a nt i n s ig h t t ha t e m e r g e s f r o m t h i s p a p e r i s t h a t C o l e m a n m a y b e s e e n a s a n a n a l y s to f s o c i a l f i e ld s . S p e c i f i c a l l y , h i s m a s t e r c o n c e p t s a r e s e e n t o b e c o n s i s t e n t w i t h c o r -r e s p o n d e n c e a n a l y s i s , a n d i n f a c t (i n th e s e n s e s p e c i f i e d ) i d e n t i c a l t o a s i n g u l a r v a l u ed e c o m p o s i t i o n - b u t w i t h s o m e q u e s t i o n s c o m i n g i n t o p l a y w h e n t h i s w o r k i s r e a df r o m a p e r s p e c t i v e c o n g e n i a l t o B o u r d i e u ' s . C o l e m a n ' s e m p h a s i s o n d u a l i t y ( f o re x a m p l e , h i s ' p o w e r ' a n d ' v a l u e ' a s s o l u t i o n s t o a s i n g u l a r v a l u e d e c o m p o s i t i o n o fm a t r i x p r o d u c t s b a s e d o n r e l a t io n s o f a c t o r s a n d r e s o u r c e s c o n c e i v e d a s c o - c o n s t i -t u t i n g o n e a n o t h e r ) i s a h i g h l y i n n o v a t i v e c o n t r i b u t i o n . B u t o n t h e o t h e r h a n d , t h em o s t o b v i o u s q u e s t i o n a r is i ng f r o m t h e f r a m e w o r k o f th i s p a p e r is : w h y d o e s C o l e -

~3 I am no t arguing tha t Bou rdieu was aware of the mathematical relations between correspondenceanalysis and rational choice models such as Colem an's (indeed, see no te 1 above), but rather tha t ana-lysts who are aware o f these relations can see important elemen ts of utilitarianism (such as equilibrium,and a micro-m odel n which actors trade forms of capital in order to enha nce their position) as 'built in 'to the m ost important quantitative methods that he deploys in his emp irical work.


18/25

10 8 R.L. Breiger / Poet ics 27 (2000) 91-115

m a n s t o p w i t h j u s t o n e d i m e n s i o n f o r h i s a n a l y s i s o f s o c i a l a c t i o n ? I n C o l e m a n ' s( 1 9 9 0 : 7 1 3 - 7 1 5 ) b r i e f a n a l y si s o f d a t a f r o m t h e G e n e r a l S o c ia l S u r v e y o n t h e v a lu e so f w o r k e r r e s o u r c e s ( e d u c a ti o n , e x p e r i e n c e ) a n d j o b r e s o u r c e s ( w a g e s , o c c u p a t io n a lp r e s t ig e ) , f o r e x a m p l e , h e d e r i v e s v a l u e s f o r t h e s e re s o u r c e s o n b o t h ' s i d e s ' o f th ee x c h a n g e o r m a t c h i n g p r o c e s s , in a g e n e r a li z a t io n o f th e a p p r o a c h r e v i e w e d h e re . I fo n e w e r e t o c o n s i d e r d i m e n s i o n s b e y o n d t h e fi rs t, i t m i g h t b e p o s s i b l e to v i e w t h el a b o r m a r k e t a s a d i f f e r e n t i a t e d ' s p a c e ' o f w o r k e r s a n d j o b s t h e m o s t i n t e r e s t i n gc h a r a c t e r i s t i c o f w h i c h m i g h t b e i t s i n h o m o g e n e i t y w i t h r e s p e c t t o w h a t i s v a l u e d ,a l o n g w h i c h d i m e n s i o n s , b y w h o m , a n d i n r e l a t i o n t o w h i c h o t h e r c o n s t r u c t o r s o fv a l u e . T h e f o c u s o n p o w e r a n d v a l u e a s m a g n i t u d e s tha t, I hav e a rgued , i s bu i l t in toC o l e m a n ' s f o r m a l a p p r o a c h s e e m s s i m i l a r t o B o u r d i e u ' s ( 1 9 9 0 b : 1 2 8 ) s p e c i f i c a t i o no f th e ' f i r s t d i m e n s i o n ' o f w h a t h e t e rm s t h e ' o v e r a l l s o c i a l s p a c e ' a s c o m p r i s e d o f" t h e o v e r a l l v o l u m e o f t h e c a p i t a l t h a t ... [ a g e n ts ] p o s s e s s " . C r u c i a l ly i n a d d i t io n ,h o w e v e r , B o u r d i e u f o c u s e s o n a s e p a r a t e d i m e n s i o n p e r t a i n i n g t o " t h e s t r u c t u r e o fthe i r cap i ta l, tha t i s . . . . the r e la t ive w e igh t o f the d i f f e r en t k inds o f cap i ta l , econ om ica n d c u l t u ra l , i n th e t o t a l v o l u m e o f th e i r c a p i t a l " ( B o u r d i e u , 1 9 9 0 b : 1 2 8) .F o u r t h , i n s y m m e t r y w i t h m y f i r s t o b s e r v a t i o n : i s i t p o s s i b l e t o s e e B o u r d i e u a st h e th e o r is t w h o s u p p l ie s th e c a u s a l fo u n d a t i o n s o f C o l e m a n ' s m o d e l ? T h i s q u e s t io nf o l l o w s f r o m r e c o g n i t i o n ( p r e v i o u s o b s e r v a t i o n ) t h a t C o l e m a n i s a t h e o r i s t o f s o c i a lf i e l d s b u t o n e w h o d o e s n o t c o n c e p t u a l i z e t h e i r m u l t i d i m e n s i o n a l n a t u r e . I n e c o -n o m i c t h e o r y a v a l u e d g o o d h a s ' a s i n g l e p r i c e ' a t e q u i l i b r i u m ( C o l e m a n , 1 9 9 0 :6 8 2 ) . I n c o n t ra s t , t h e v a l u e s i n t h e s p a c e o f c o r r e s p o n d e n c e s t h a t B o u r d i e u c o n s t r u c t sa r e a l w a y s p o l y s e m o u s , m u l t i d i m e n s i o n a l , c a r r y i n g d i f f e r i n g m e a n i n g s w i t h r e s p e c tt o a s s o c i a t e d p ri n c i p l e s o f a c t i o n a n d c o n t r a d i c t io n s a m o n g t h o s e p r i n c ip l e s , a n dl i k e l y t o b e i n t e r p r e t e d d i f f e r e n t l y w i t h r e s p e c t t o a c t o r s ' d i s t i n c t i v e l o c a t i o n s i n as o c i a l o r c u l t u ra l f i el d . 14 T h i s p o i n t a l o n e m a r k e d l y d i s ti n g u i s h e s B o u r d i e u ' s t e c h -n i q u e f r o m t h e m o d e l i n g f r a m e w o r k o f e c o n o m i c s , a n d p r o v i d e s o n e s o r t o f g r o u n d-i n g f o r B o u r d i e u ' s s u g g e s t i o n t h a t " f a r f r o m b e i n g t h e f o u n d i n g m o d e l , e c o n o m i ct h e o r y ( a n d r a t i o n a l a c t i o n t h e o r y w h i c h i s i t s s o c i o l o g i c a l d e r i v a t i v e ) i s p r o b a b l ybes t s een as a pa r t icu la r ins tance , h i s to r ica l ly da ted and s i tua ted , o f f i e ld the ory "s u c h a s h i s o w n ( q u o t e d in C a l h o u n , 1 9 9 3 : 8 5 - 8 6 ) . A f u r t h e r a rg u m e n t f o r p o r t r a y -i n g B o u r d i e u a s p r o v i d i n g ( i n e f f e c t ) t h e c a u s a l f o u n d a t i o n s f o r C o l e m a n ' s f r a m e -w o r k i s t h a t , i n h i s m a j o r w o r k D i s t i n c t i o n B o u r d i e u ( 1 9 8 4 [ 1 9 7 9 ] ) h a s e l a b o r a t e d ac o m p r e h e n s i v e t h e o r y o f h o w i t i s t h a t p e o p l e a n d s o c i a l g r o u p s t e n d t o v a l u e c e r t ai nk i n d s o f o b j e c t s a n d o u t c o m e s o v e r o t h e rs - j u s t t h e k i n d o f t h e o r y o f v a l u a t i o n t h a ti s n e c e s s a r y b u t e x o g e n o u s to C o l e m a n ' s ( 1 9 9 0 ) s p e c i f i c a t io n o f t h e ' I n t e r e s t'm a t r i x , a n d a t h e o r y t h a t i n B o u r d i e u ' s f o r m u l a t i o n i s i n t i m a t e l y r e l a t e d t o d o m i n a -t i o n o r ' c o n t r o l ' a s w e l l a s t o ' i n t e r e s t ' .F i f t h , i t s e e m s c l e a r t h a t c u l t u r a l a n a l y s i s w o u l d b e n e f i t f r o m a t h e o r y o f s o c i a lm e a s u r e m e n t a n d m e a n i n g r e l e v a n t t o th e i s s u e s i n t h i s p a p e r . I d o n o t h a v e i n m i n dt h e u n i fi c a t io n o f B o u r d i e u ' s a n d C o l e m a n ' s s o c i a l t h e o r i e s in s o m e s in g l e f r a m e -~4 A n i n t e rp re ta t io n o f Bo u rd i eu ' s w o rk t h a t emp h as i ze s t h e i mp o r t an ce o f t h e du a l r o le s o f ti me an ds p ace ( l o ca t io n , co n cen t r a ti o n , s y n ch ro n i za t io n , p ace ) i n Bo u rd i e u ' s t h in k i n g ab o u t b o t h t h e ma t e r i a l an dthe logica l in tegra t ion of ac t ion i s tha t o f Fr i edland and Boden (1994: 21-23) . See a l so Abbot t (1997) .


19/25

R.L. Breiger / Poetics 27 (2000) 91-115 109work, as I am convinced that such a project would do symbolic violence to bothschemes. Within the framework of this paper, what seems most necessary is a mod-eling context that brings a concern with dimensions underlying the m a r g i n a l s ofrelational fields (similar to Coleman's 'power') within the same scope as a concernfor d i m e n s i o n s for social proximities and profiles (as in Bourdieu's use of CA). Iwould put forward as an example of this kind of work the analysis in Han andBreiger (1999; building on Breiger and Ennis, 1997; Breiger and Roberts, 1998) ofrelations among investment banks formed in 'doing deals', where both kinds ofdimensions are delineated within a single model of exchange and hierarchy.

A point related to the fifth observation is that neither Bourdieu nor Coleman, inthe work reviewed here, provides a statistical framework within which the relevanceof their formal methods to data might be assessed. However, a great deal of work inthe area of loglinear models and related methods (see in particular Goodman, 1996)has gone into formulating related statistical models. Techniques used by Han andBreiger, unlike those employed by either Bourdieu or Coleman, implement loglinearmodels that allow answers to the question of how well a model fits the data.

5 . P r a c t i c a l m e t h o d s a n d m e t h o d o l o g i c a l p r a c t i c eSocial and cultural analysts well know that issues of theoretical orientation are

matters of contention and worth fighting over. When it comes to quantitative meth-ods, however, we often assume (even while occasionally being content to condemnsuch methods out of hand) that styles of quantification are entirely irrelevant to the-oretical and ideological struggles. Such an assumption is not productive. Interpreta-tion of quantitative methods is inseparable from more usual forms of textual inter-pretation, and on occasion interpretation of an author's methods of quantification candeeply enrich our reading and writing of social and cultural theory.

Both Coleman and Bourdieu are important structuralist thinkers of the twentiethcentury. The difference between them for present purposes is that Coleman, who hadearlier been an inventor of contextual analysis (Coleman, 1958-1959:30-31) and afather of network analysis, sought in his later work, for bold and principled reasonshaving to do with his beliefs about what is most necessary for the development ofsocial theory (Coleman, 1990: 650-664), to push structural analysis further and fur-ther toward generalizations removed from the context of time and place; Bourdieu,on the other hand, and despite notable counter-tendencies, seeks to push structuralistanalysis as far as possible in the direction of analyzing practical actors, performance,meaningfulness as a social product, and interpenetration of cultural and symbolicaction.In this paper (section 2 above) Bourdieu and Coleman have been so-to-speakcaught assigning the same numbers, to however many decimal places one cares totake account of, to methodological procedures which they and everyone else claim tobe entirely different. What is the meaning of this? The meaning is up for negotiation,and I endeavor to negotiate these shoals in section 4. Is Bourdieu a rational choicetheorist? Can Coleman be claimed as a field theorist by institutionalists interested in


20/25

110 R.L. Breiger / Poetics 27 (2000) 91-115t h e p r a g m a t i c s o f p e r f o r m a n c e ? A s k i n g t h e s e q u e s t i o n s , a n d m o r e g e n e r a l l y u s i n gq u a n t i t a t i v e a n a l y s i s a s p r o v i d i n g f r a m e w o r k s f o r p r o b i n g s o c i a l a n d c u l t u r a l t h e o r ya n d a s a m e a n s f o r t h e c o m p a r i s o n a n d i n t e r ro g a t i o n o f t e x t s, a re s o m e o f th e g a i n sf r o m r e c o g n i z i n g t h a t q u a n t i t a t i v e a p p l i c a t i o n s t h e m s e l v e s a r e c a r d e d o u t w i t h i nd o m a i n s o f s o c i a l p r a c t i c e s a n d c u l t u r a l s y m b o l s . R e a d i n g ' a c r o s s ' m e t h o d o l o g i c a lt r a d i t i o n s c a n y i e l d n e w i n s i g h t s a n d n e w t o o l s , s u c h a s t h e p r o p o s e d s y n t h e s i s ( i ns e c t i o n 3 o f th i s p a p e r ) o f G a l o i s l a t ti c e a n a l y s i s w i t h c o r r e s p o n d e n c e a n a l y s i s a n dr e l a te d p r o c e d u r e s .S e v e r a l s t o r i e s m i g h t b e , a n d a r e , t o l d a b o u t e i g e n v e c t o r s . T h e y a r e t h e l o w -d i m e n s i o n a l s c a f f o l d s t h a t s u p p o r t h i g h e r - d im e n s i o n a l s t ru c t u r e s ( se e A p p e n d i x A ) .T h e y i n d e x t h e d i m e n s i o n s o f B o u r d i e u ' s s o c i a l fi e ld s . T h e y a r e, i n B o u r d i e u ' s( 1 9 8 4 [ 1 9 7 9 ] ) a p p l i c a ti o n o f c o r r e s p o n d e n c e a n a l y s is , a " v i s u a l i z a t i o n o f p r o x i m i t i e sb e t w e e n s p e c i f i c r e s p o n s e l e v e l s o f a q u e s t i o n n a i r e a n d c h a r a c t e ri s ti c s o f t h e r e s p o n -d e n t s " , d e m o n s t r a t i n g t h e a s s o c i a t i o n b e t w e e n c e r t a in t y p e s o f c u l t u ra l p r o f i le s a n dcer ta in soc ia l s i tua t ions (van Mete r e t a l . , 1994: 133) . They a r e the we igh ts tha td e f i n e a c t o r s ' c e n t r a l i t y r e c u r s i v e l y ( R o s e n t h a l e t a l . , 1 9 8 7 ) . T h e y a r e t h e e q u i l i b -r i u m o u t c o m e o f e x c h a n g e s i n a m a r k e t o f r a ti o n a l t r ad e r s ( p o i n t o n e i n s e c t i o n 4a b o v e ) . T h e y a r e f u n d a m e n t a l t o v o n N e u m a n n ' s m o d e l o f a n ex p a n d i n g e c o n o m ya n d t o L e o n t i e f 's m o d e l o f e q u i l ib r i u m e x c h a n g e s a m o n g e c o n o m i c s e c to r s (S t ra n g ,1 9 8 0 : 2 0 3 - 2 0 4 ) . I n C o l e m a n ' s ( 1 9 9 0 ) m o d e l t h e y p r o v i d e t h e m a c r o - s t r u c t u r e o fa c t o r s ' p o w e r a n d e v e n t s ' v a l u e t h a t e m e r g e s f r o m a c t o r s ' m i c ro - l e v e l e x c h a n g e s o fc o n t r o l o n t h e b a s i s o f r a ti o n a l p u r s u i t o f i n d i v i d u a l s ' i n t er e s ts . L i k e o t h e r k i n d s o fs t o ri e s , st o r ie s a b o u t a p p l i c a b l e m e t h o d s a r e u n d e r d e t e r m i n e d ( t h e y a re n o t s e l f - c o n -ta ined na r r a t ives ) . S tor ie s a r e cons t i tuen t s o f soc ia l space s (W hi te , 1992: 68) , bu tt h e y d o n ' t f u l l y s u s t a i n t h e m s e l v e s i n t e rn a l ly . T h e y e x i s t w i t h i n s o c i a l f i e ld s . W h i c ho n e a p p l i e s t o s o m e r e s e a r c h p r o b l e m a t h a n d ? T h e s e s t o r i e s n e e d t o b e c o n t e x t u a l -i z e d, w i t h p l o t li n e s j o i n e d o r s e p a r a t e d a s a p p r o p r i a te , b y r e s e a rc h e r s w o r k i n g u n d e rpa r t i cu la r soc ia l and cu l tu r a l p r ac t i ces - tha t i s , by pr ac t i ca l r e sea rcher s . The ab i l i tyt o c o m p r e h e n d a v a r i e t y o f g e n r e s a n d p l o t l i n e s a n d t o c o n t r i b u t e t o t h e m w i l l c o n -t inue to d i s t inguish imp or tan t w ork (Cicoure l , 1993) .S w i d l e r ' s ( 1 9 8 6 : 2 7 9 , 2 8 1 ) i d e n t i fi c a t io n o f t w o c o n t r a s t in g m o d e s o f c u lt u r e -c u l t u r e a s s y s t e m ; c u l t u r e a s t o o l k i t - f i n d s a r e f l e c t io n i n c u l t u re s o f m e t h o d o l o g i -c a l a n a ly s i s . O n c e i t is re c o g n i z e d , h o w e v e r , t h a t d i ff e r e n t ' l o g i c s ' o f m e t h o d s e x i s t ,c h o o s i n g b e t w e e n t h e m r e q u i r e s , s o t o s p e a k , s t e p p i n g o u t s i d e t h e i r s c o p e ( D i M a g -g i o , 1 9 9 2 ) a n d r e c o g n i z i n g t h a t o n e h a s b e c o m e a p ra c t ic a l a c t o r, a n a c t o r c a p a b l e o fc h o o s i n g a p p r o p r i a t e l y a s w e l l a s c o r r e c t l y .I want to conc lude th i s a r t i c le in the spec ia l i s sue of Poetics b y p o i n t i n g o u t t h a tC u l l e r ( 1 9 9 7 : 7 5 , 7 8 ) i d e n t i f ie s a s a m a j o r p r o b l e m f o r th e t h e o r y o f p o e t r y t h e r e la -t i o n b e t w e e n t h e p o e m a s a s t r u c t u r e m a d e o f w o r d s ( a t e x t ) a n d t h e p o e m a s a ne v e n t ( a n a c t o f th e p o e t , a n e x p e r i e n c e o f th e r e a d e r , a n e v e n t i n li t er a ry h i s t o r y ; s e ea l s o J a k o b s o n , 1 9 9 0 [ 1 9 6 0 ] ) . L i k e w i s e , it is i m p o r t a n t t o r e c o g n i z e t h a t q u a n t it a t iv em e t h o d s c o n s i s t o f a f o r m a l s t r u c tu r e ( a m a t h e m a t i c s ) a n d a n e v e n t ( a n a p p l ic a t i o nto a da tase t , a l inkage to ano the r ma themat ica l s t r uc tur e , an incorpora t ion wi th in as o c i a l o r c u l t u r a l s t o r y ) . T h e r e l a t i o n b e t w e e n s t r u c t u r e a n d e v e n t i s p r o b l e m a t i c i nw a y s t h a t a r e h i g h l y p r o d u c t i v e o f s o c i o l o g i c a l a n a ly s i s. T h i s i s p r e c i s e l y t h e s o r t o f


21/25

R.L. Breiger / Poet ics 27 (2000) 91-1 15 111

p r o b l e m t h a t n e e d s t o b e a d d r e s s e d i n a p r a c t i c al t h e o r y o f r e s e a r c h m e t h o d s , a n d i ti s n o t t o o f a r o f f f r o m t h e p r o b l e m a t i c s o f p r a c ti c e t h e o r y m o r e g e n e r a l l y .

A p p e n d i x A : A g l o s s o n t h e m a t h e m a t i c s o f c o r r e s p o n d e n c e a n a l y s i s a n d r e l a te d m o d e l sT h e f o l l o w in g n o n - m a th e m a t i c a l g lo s s o n m a th e m a t i c s m ig h t b e u s e f u l f o r r e a d e rs u n f a -m i l i a r w i th t h e s e c o n c e p t s . T o p u r s u e m a t t e r s f u r th e r , o n e m ig h t c o n s u l t a n i n t r o d u c to r y tr e a t-

m e n t s u c h a s D ig b y a n d Ke m p to n ( 1 9 8 7 : 1 9 3 - 2 0 3 ) , Ro s e n th a l e t a l . ( 1 9 8 7 ) , o r W e l l e r a n dR o m n e y ( 1 9 9 0 ) . F o r p u r s u i t o f t h e se i s s u e s b e y o n d t h e i n t r o d u c to r y le v e l, I r e c o m m e n d t h es u b s t a n ti v e p a p e r s o f M a r s d e n a n d L a u m a n n ( 1 9 7 7 ) a n d T a m ( 1 9 8 9 ).A . 1 . S i n g u l a r v a l u e d e c o m p o s i t io n

L o o s e ly s p e a k in g , a n e i g e n v e c t o r o f a s q u a re , s y m m e t r i c m a t r ix M i s a s t r in g o f n u m b e r s- that is , a v e c t o r - t e r m e d s = (s l , s2 . . . . sn) such tha t , when m ul t ip l ied by i t se l f - so tha t ince l l ( i , j ) we have the p roduc t s i x s j - the resu l t is a ' be s t ' r ep resen ta t ion o f the o r ig ina l ma t r ixM ( ' b e s t ' b y t h e c r i te r i o n o f l ea s t s q u a r e s : t h e s u m o f s q u a r e d d if f e r e n c e s b e twe e n c e l l s o f Ma n d c e l l s o f t h e r e p r e se n t a t io n i s s m a l le r w i th o u r c h o i c e o f s t h a n w i th a n y o th e r c h o i c e ) .T h i s i s i n f a c t t h e ' f i r s t ' e i g e n v e c to r . T h e ' s e c o n d ' m a y b e f o u n d b y c o m p u t in g a n e ig e n v e c -to r f r o m th e r e s idu a l s p r o d u c e d i n s u b t r a c t in g f r o m M th e r e p r e s e n t a ti o n d e f i n e d a b o v e ( o r b yc o m p u t in g a n e ig e n v e c to r o n r e sid u a ls f r o m th e c o m p a r i s o n o f M to t h e r e p r e s e n t a ti o n c o m -p o s e d o f t h e f i r s t k e ig e n v e c to r s , w h e n c o n s t r u c t i n g t h e k + 1s t. ). In th is sense , the ' f i r s t ' e igen-v e c to r p r o v id e s a ' b e s t ' r e p r e s e n t a t i o n o f a m a t r ix b y m e a n s o f a s in g l e s t ri n g o f n u m b e r s .As s o c i a t e d w i th e a c h e ig e n v e c to r i s a we ig h t ( a s i n g l e n u m b e r ) , t e r m e d a s i n g u l a r v a l u e ,r e f l e c t i n g t h e e x t e n t t o wh ic h t h a t v e c to r c o n t r i b u t e s t o a c c o u n t i n g f o r t h e a s s o c i a t i o nb e t w e e n r o w s a n d c o l u m n s o f M . D e f i n e th e s i n g u l a r v a l u e d e c o m p o s i t i o n ( S V D ) o f a r ec -t a n g u l a r m a t r i x A h a v in g n r o ws a n d m c o lu m n s t o b eA = U S V TI n t h is r e p r e s e n ta t i o n , t h e c o lu m n s o f m a t r ix U a r e t h e e ig e n v e c to r s o f th e s q u a r e s y m m e t r i cm a t r i x AAr , where the supersc r ip t T re fe rs to tak ing the t ranspose o f mat r ix A. Dua l ly , thec o lu m n s o f m a t r ix V ar e t h e e ig e n v e c to r s o f th e s q u a r e s y m m e t r i c m a t r i x A r A . ( I f th e s e c o n -c e p t s a p p e a r f o r e ig n , p e r h a p s t h i s e x a m p le w i l l h e lp . I f r o ws o f A d e n o t e o c c u p a t i o n s a n dc o lu m n s d e n o t e p o s s ib l e s u b j e c ts o f b e a u t if u l p h o to g r a p h s , t h e n t h e c e l ls o f AA c o n n e c t e a c hp a i r o f o c c u p a t i o n s b y t h e e x t e n t t o wh ic h t h e i r i n c u m b e n t s c h o o s e s im i l a r s u b j e c t s a s b e a u -t i fu l . And the ce l l s o f A r A c o n n e c t e a c h p a i r o f p h o to g r a p h s u b j e c ts b y t h e e x t e n t t o wh ic hth e y a r e j o in t l y c h o s e n b y m e m b e r s o f t h e s a m e o c c u p a t i o n . ) M a t r i x S h a s z e r o s e v e r y wh e r ee x c e p t o n i ts d i a g o n a l , wh ic h c o n s i s t s o f t h e s i n g u la r v a lu e s a s s o c i a t e d w i th t h e e ig e n v e c to r si n U ( wh ic h t u r n o u t b y a m a th e m a t i c a l d u a l i t y t o b e i d e n t i c a l t o t h e s i n g u l a r v a lu e s a s s o -c ia ted wi th the e igenvec to rs in V) .A . 2 . T h e f i r s t d i m e n s i o n o f S V D p e r t a i n s t o th e m a r g i n a l s

I n e s t im a t i n g a s im p le r e g r e s s io n e q u a t i o n , t h e ' b e s t ' r e p r e s e n t a t

b reiger toolkit

Documents